Related papers: Binary Cumulant Varieties
Hyperuniform states of matter exhibit unusual suppression of density fluctuations at large scales, contrasting sharply with typical disordered configurations. Various types of hyperuniformity emerge in multicomponent disordered systems,…
In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy…
We present an algorithm for solving binary classification problems when the dataset is not fully representative of the problem being solved, and obtaining more data is not possible. It relies on a trained model with loose accuracy…
We study families of algebraic varieties parametrized by topological spaces and generalize some classical results such as Hilbert Nullstellensatz and primary decomposition of commutative rings. We show that there is an equivalence between…
We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relations for classical constructions of corresponding spanning…
Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector…
Non-degenerate bilinear forms over fields of characteristic 2, in particular, non-symmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are…
We investigate conditions for the existence of the limiting conditional distribution of a bivariate random vector when one component becomes large. We revisit the existing literature on the topic, and present some new sufficient conditions.…
In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant $2$, and provide a database of such bases. One of our motivations is…
We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…
We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the…
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…
We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants.
A binary tensor consists of $2^n$ entries arranged into hypercube format $2 \times 2 \times \cdots \times 2$. There are $n$ ways to flatten such a tensor into a matrix of size $2 \times 2^{n-1}$. For each flattening, $M$, we take the…
A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the…
This text is a draft of the review paper on projectively dual varieties. Topics include dual varieties, Pyasetskii pairing, discriminant complexes, resultants and schemes of zeros, secant and tangential varieties, Ein theorems, applications…
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
Binary regression models are ubiquitous in virtually every scientific field. Frequently, traditional generalized linear models fail to capture the variability in the probability surface that gives rise to the binary observations and novel…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…